As a substrate for a liquid crystal displaying element, an electronic displaying element such as an organic EL displaying element, an electronic optical element such as CCD or a CMOS sensor, or a solar battery, a glass plate has been conventionally used due to its high thermal stability, high transparency and low moisture permeability. However, as portable information devices or a cell phone prevail in recent years, a substrate, which is light, flexible, and tough, has been required as a substrate thereof in place for a glass plate, which is relatively heavy and fragile. So, plastic substrates such as a polyethersulfone substrate, a polycarbonate substrate, and a laminate of a polyethersulfone plate with an acryl resin plate as disclosed in Japanese Patent O.P.I. Publication No. 5-142525, have been proposed and put into practical use. However, their high price and their poorness of optical properties such as light transmittance and birefringence have been an obstacle to prevalence of these substrates. Further, since these plastic substrates have a negative wavelength dispersion property, compensation of polarized light cannot be made over the entire visible wavelength region in a liquid display employing a birefringence image displaying method, for example, a liquid display of a STN mode, a VA mode or an IPS mode, resulting in color deviation of a displaying color image, and contrast are lowered in an organic EL displaying element. As a resin having a positive wavelength dispersion property there are mentioned cellulose derivatives, for example, cellulose acetate propionate, however, these cellulose derivatives are not suitable for a substrate of image displaying elements on account of their too high moisture permeability.